A modified grasshopper optimization algorithm combined with wavelet functions

The present study analyzes the social interaction function of grasshoppers using five alternative wavelet functions for the original function of grasshoppers. In this research, the Morlet, Polywog1, Polywog3, Rasp1, and Rasp3 wavelet functions have been selected as possible substitutes for the wavelet function. The first structure is a three-member truss, it is optimized under the constraints of tension, deformation, and buckling, to reduce the weight of the truss. The second structure is a cantilever beam, with five hollow square beam sections, with the target function aiming to minimize the total weight of the beam. This research aims to present a proposed model combining the grasshopper algorithm and wavelet functions to improve the convergence speed and results of the grasshopper algorithm. The research results show that replacing the wavelet functions does not change much in the weight of the first benchmark structure, but it provides acceptable accuracy. The Polywog1 algorithm demonstrates superior performance, converging faster than GOA, with a marginal difference of 2.64×10^-8 percent in weight. In addition, the Rasp3 algorithm shows the best result with 6.46×10-10 percent more weight than GOA. In the cantilever beam structure, the optimization has been improved and, in all cases, the convergence speed has been evaluated as appropriate. Moreover, only Morlet wavelet functions have provided a suitable solution while other wavelet functions have not been successful in this field. Adding wavelet functions as the interaction function of the grasshoppers removes the source of error, which includes the l and f parameters, in the new possible functions.